Vortragszusammenfassung

Mathematical models of ice formation inside and outside of living cells during freezing and thawing are derived by applying an appropriate averaging technique to partial differential equations describing the dynamics of water-to-ice phase change. This reduces spatially distributed relations to a few ordinary differential equations with control parameters and uncertainties. Such equations together with an appropriate objective functional that expresses some injuring effect of cell freezing or thawing are considered as a differential game where the aim of the control is to minimize the objective functional, and the aim of the disturbance is opposite. A stable finite-difference scheme for computing the value function of the game is developed. On the base of the computed value function, optimal cooling and thawing protocols are designed. This is a joint work with N.D.Botkin and K.-H.Hoffmann.